Whatever happened to the original point of all this, which I seem to remember (could be wrong!) was something like:
Preearth says the gravitational potential energy of two planets moving from very close to combining may not be converted into enough heat to melt the crust.
Somebody else saying the gravitational potential energy of the two planets moving from very close to combining would have to be converted to enough heat to melt the crust.
How about a simple calculation like this:
1) Find the gravitational potential energy of the two planets just touching (using several methods if need be)
2) Find the gravitational potential energy of the combined planet (using the same method(s) as in 1).
3) Find the difference, and make sure it's the same for all methods. If not, got back and identify the wrong ones.
4) Assume all the energy is converted to heat and so find the amount of heat energy created
5) Estimate an upper bound on the time taken to combine.
6) Apply a radiative cooling model (or a suitable approximation), and calculate the temperature gradient through the surface of the combined planet.
7) See if the surface of the combined planet has a layer of similar thickness to continental crust which never exceeds the melting point of that material.
8) Conclude that the energy calculation either disproves Preearth's hypothesis, or is compatible with it.
Easy peasy!! Who wants to work through this with me?
Bonus part) If it disproves it, then increase the time taken to combine. For a slow enough process it won't disprove the hypothesis. This can give a quantified lower limit on the time taken to combine.
Last edited by kallog; 02/15/11 05:01 AM.
